Calendar Cubes

My grandmother has a pair of calendar cubes; each cube has six digits on it, one on each face.
Every morning, she re-arranges them to show the day of the month as a two-digit number (01 to 31).

Even though some numbers appear on both cubes, you can easily tell them apart because one cube is ivory and the other is brown.
I noticed that it was possible to use the ivory cube in the tens place and the brown cube in the ones place for SEVEN days in a row (within one month)!
Can you figure out what digits are on each cube?

Hint

Both cubes need a 1 (to form 11) and a 2 (to form 22).
The 0 must be paired with every other digit, so it must be on both cubes too.
This leaves six spaces (three on each die) to fit seven digits (3, 4, 5, 6, 7, 8, 9).
One digit can be re-used in an interesting way!Hide